In many dog owners' lives there exist intrepid canines who refuse to be contained. You, dear human, are such a silly worry wart to these dogs' way of thinking. They know how to handle themselves in the big bad world, and they take every opportunity to prove it.
Independent, runaway dogs will dig, climb, and scoot their way to freedom, sometimes destroying fencing as they escape. The damage and liability they create while on the loose are reasons enough to want a solid solution to the problem.
Apply a double escape deterrent
Don't rely on one form of containment for stubborn roamers. If your dog regularly digs under the most solid privacy fence, new dirt or fence panels won't fix the problem. Solve a digging problem with a strip of lightly charged electrical tape along the bottom of the fencing. Most dogs will avoid the shock and stop digging.
You can also staple a run of poultry wire to the bottom edge of wood fencing, then bend and bury the lower part under the area where the dog digs. They'll uncover the wire but won't be able to dig through it.
Use a three-pronged approach if necessary
An electronic fencing system that relies on a battery-operated collar is often enough of a deterrent for most dogs. Add an extra layer with a six-foot chain link fence for the dog who regularly climbs. Chain link is not as easy for dogs to chew their way through as wood or vinyl fencing can be.
If you have a dog who digs, climbs and chews, add a strip of tape on the bottom of the fence line to the collar/chain link combo. It must be grounded. of course, and be mounted on plastic brackets or step in posts set close to the digging area.
Having three steps to master often delays or completely discourages a stubborn pup. Some owners report that the dogs will later associate even un-charged tape as "off limits," so a short period of using the tape will pay off in the future when you outwit the dog for a change.
Sometimes it's the terrain
If you live in an area with lots of boulders and rocks, you may have a tough time making solid, dog-proof fences. It's not easy installing posts in stony ground. There are ways to set posts in this type of terrain, and there are numerous methods that don't require posts, but you will invest a lot of labor to anchor fencing properly.
One solution to a rocky terrain is using a double electronic fence. You set an inner and outer perimeter, and both alert when they've been breached. A system like this may be all you need and will buy you time to construct a more solid fence.
Talk to your dog fencing professionals about the various methods of containment for your dog's breed and type. They have experience and sources of fencing solutions for most fence-defying dog situations. Check it out on websites like this one.